Sir Hugh Robertson, chair of the BOA, said the decision from the Court of Arbitration for Sport (CAS) was "reassuring" in the fight for clean sport.
"There was no finding that it was carried out in a discriminatory, arbitrary or unfair manner", he said.
It invited 169 carefully screened Russian athletes to compete as neutrals under the Olympic flag. "The [CAS] panel also concluded that there was no evidence that these two commissions improperly exercised their discretion".
However, the panel allowed 168 athletes to participate in the Winter Olympics as scheduled.
"It's hard for CAS to make decisions against the backdrop of an earlier pressure", Russian Deputy Prime Minister Vitaly Mutko told Interfax news agency, referring to objections from the International Olympic Committee.
A spokesman for the Olympic Athletes from Russia told AFP: "It's a pity the Russian delegation is not bigger".
"The athletes are sort of celebrating the decision in a way", said America's Angela Ruggiero, chair of the International Olympic Committee athletes commission.
The aforementioned 15, including two coaches, were entering a second appeal after the IOC's invitation review panel decided not to invite them to Pyeongchang, even though CAS upheld their initial appeal on February 1, saying there was insufficient evidence to prove they violated anti-doping rules.
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"The IOC has been working extraordinarily hard to make sure that we protect the clean athletes", she said. "We want our athletes to be competing against the very best but in the knowledge they are facing clean athletes". Russian competitors marched behind a neutral Olympic flag at Friday's opening ceremony.
The Russians also lodged a further case with a Swiss civil court in Lausanne, where the International Olympic Committee is headquartered, in a final bid to compete in South Korea.
"The applications filed by Russian athletes and coaches have been dismissed", CAS secretary general Matthieu Reeb told a packed news conference. Fifteen other athletes and coaches who recently had their sanctions overturned by CAS also appealed.
At a news conference Thursday, officials from the World Anti-Doping Agency both defended the slow conclusion to the Russian Federation case and expressed frustration with the process. Individual athletes were given permission to take part in the games, provided they take a test to determine they haven't violated the doping rules.
However, the CAS decision may not be the end of the matter.
Russia's participation has been fiercely debated among athletes and Canada's team was forced to apologise on Thursday after an alleged altercation at the athletes' village. Specifically, Russian officials have not publicly accepted the findings of Richard McLaren, a Canadian professor who outlined the state-sponsored doping system in an independent report in 2016, nor have they allowed WADA officials access to a Moscow laboratory where urine and blood samples of Russian athletes are stored.
People walk past the emblem of the 2018 PyeongChang Winter Olympics.